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A363463
a(n) is the smallest number k with exactly n of its divisors in A052294.
0
1, 3, 6, 12, 18, 48, 36, 192, 72, 84, 144, 3072, 168, 5985, 576, 336, 504, 26505, 672, 45045, 840, 1344, 6510, 129675, 2016, 1680, 11970, 4620, 4032, 389025, 3360, 888615, 6552, 13020, 53010, 6720, 8736, 855855, 90090, 23940, 13104, 2411955, 17472, 2417415, 26040
OFFSET
0,2
EXAMPLE
a(0) = 1 because 1 has no divisors in A052294.
2 has no divisors in A052294 and 3 has only one divisor 3 = 11_2 in A052294, so a(1) = 3.
4 has no divisors in A052294, 5 has only the divisor 5 = 101_2 in A052294, 6 has divisors 3 = 11_2 and 6 = 110_2, so a(2) = 6.
MATHEMATICA
seq[len_, kmax_] := Module[{s = Table[0, {len}], c = 0, k = 1, ind}, While[k < kmax && c < len, ind = DivisorSum[k, 1 &, PrimeQ[DigitCount[#, 2, 1]] &] + 1; If[ind <= len && s[[ind]] == 0, c++; s[[ind]] = k]; k++]; s]; seq[40, 10^6] (* Amiram Eldar, Jul 10 2023 *)
PROG
(Magma) fp:=func<n|IsPrime(Multiplicity(Intseq(n, 2), 1)) >; a:=[]; for n in [0..44] do k:= 1; while #[d:d in Divisors(k)|fp(d)] ne n do k:=k+1; end while; Append(~a, k); end for; a;
(PARI) a(n) = my(k=1); while (sumdiv(k, d, isprime(hammingweight(d))) != n, k++); k; \\ Michel Marcus, Jul 10 2023
CROSSREFS
Cf. A052294.
Sequence in context: A298029 A327328 A356019 * A074899 A345868 A318872
KEYWORD
nonn,base
AUTHOR
Marius A. Burtea, Jul 08 2023
STATUS
approved